In the middle of a rather technical article (diagrams maybe not safe for work) about primate sexual attributes, there's some interesting stuff about polygamy (or polygyny, as monks don't get married).

Primates exhibit all sorts of mating behaviour, including monogamous, polygynous – where males have multiple mates – and multimale-multifemale. One indicator of which behaviour occurs in a species is the size difference between males and females.<snip>Male gorilla are also much larger than females, but they have a polygynous or harem-style mating system where many females live with a single male.<snip>

Monogamy mystery

This observation clashes with the fact that men are significantly larger than women. This suggests our evolutionary background involved a significant degree of polygynous, rather than exclusively monogamous, mating. This is supported by anthropological data showing that most modern human populations engage in polygynous marriage. Anthropologists Clellan Ford and Frank Beach in their book Patterns of Sexual Behaviour suggested that 84% of the 185 human cultures they had data on engaged in polygyny.

However, even in these societies most people remain monogamous. Polygynous marriages are usually a privilege reserved only for high status or wealthy men. It is worth noting that hunter-gathers around the world practice only monogamy or serial-monogamy which suggests that our ancestors may have used this mating system.<snip>So when living in complex human societies the largest and most important sexual organ is the brain. Somewhere in our evolutionary past how smart and social we are became the major control on our access to sexual partners – not how big or fancy a male’s penis is.

Monogamy as a norm is relatively young, and was really only properly established in the Greco-Roman world where monogamy was a sort of "official" norm (i.e. you could only have one legal husband or wife), but it was also much more acceptable to have "lovers" or "mistresses" or simply use prostitutes, than it is today. it really only became prominent with the rise of Christianity, and while the one marriage plus sidelines continued, that aspect kind of became semi-legal and part of a sub-culture. It is kind of strange how monogamy got into Christianity, because many biblical characters had multiple wives, and you find little to expressly demand monogamy. It arrived via the Jewish customs, and the law in the Roman world. The Jews did what they always did when faced with foreign government, they adapted and tried to fit it.

Monogamy was pretty much adopted by them to comply with Roman Law. It was not a big issue even, as since the Babylonian captivity, monogamy had been more or less the norm anyway. By the time Jesus was born it was established custom, and it was accepted as such by Jesus in his own teachings. What Christianity changed, it stressed the idea of a life long commitment and of fidelity, and some would say with only moderate success.

Polygyny is a much more ancient custom, and it was particularly useful when a lot of children were an important to guarantee survival of old age or illness. The extended family was in a sense the first social security system, and in some places it still is. It is not surprising that in societies where resources are scarce, such as Mohammed's, it survived. Arabia had not been touched by Rome, and the ancient way had worked in some ways, even though it created a land with many tribes all fighting each other.

Other systems of mutual support arose later in Christianity, such a monastic communities which also fulfilled this purpose, but this was a completely new way of life.

If you know any families with one man and several wives, you very often find the same problems, over and over: One wife feels neglected over the other, jealousies ensue, and all kinds of intrigues about inheritance and property are common. Also "pecking orders" develop among wives, who rarely manage to establish a genuine friendship and sometimes not even a working partnership. Finally, children often have different relationships with their half-siblings than their actual siblings.

I am not say it can never work, but it is a very much more difficult model than the monogamous one.